Euler, φ and ρ

[Note: I need to end the equations with a period to persuade WordPress/Latex to put sane spacing between lines.

Euler’s famous equation $e^{iπ} + 1 = 0$ is usually considered the “most beautiful” in mathematics.

We could also write it in the so-called “ugly” format as $e^{iπ} = -1$.

Now we know that for the golden ratio φ,

${1 \over {φ}} - φ = -1$.

So let’s rewrite Euler using that: